On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer

TL;DR

This paper provides a rigorous convergence analysis of the IPG observer for nonlinear systems, establishing its local linear convergence and confirming its robustness advantages over other Newton-type observers.

Contribution

It offers the first theoretical proof of convergence for the IPG observer, linking it to Newton observers and enhancing understanding of its robustness.

Findings

Proves local linear convergence of IPG observer.

Confirms relation between IPG and Newton observers.

Enhances theoretical understanding of IPG robustness.

Abstract

This paper considers the observer design problem for discrete-time nonlinear dynamical systems with sampled measurement data. Earlier, the recently proposed Iteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type observer, has been empirically shown to have improved robustness against measurement noise than the prominent nonlinear observers, a property that other Newton-type observers lack. However, no theoretical guarantees on the convergence of the IPG observer were provided. This paper presents a rigorous convergence analysis of the IPG observer for a class of nonlinear systems in deterministic settings, proving its local linear convergence to the actual trajectory. Our assumptions are standard in the existing literature of Newton-type observers, and the analysis further confirms the relation of the IPG observer with the Newton observer, which was only hypothesized earlier.